Algebra Examples

${(\frac{1}{2} y^{5})}^{3} {(2 y^{2})}^{4}$

Step 1

Combine $\frac{1}{2}$ and $y^{5}$ .

${(\frac{y^{5}}{2})}^{3} {(2 y^{2})}^{4}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{y^{5}}{2}$ .

$\frac{{(y^{5})}^{3}}{2^{3}} {(2 y^{2})}^{4}$

Step 2.2

Multiply the exponents in ${(y^{5})}^{3}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{y^{5 \cdot 3}}{2^{3}} {(2 y^{2})}^{4}$

Step 2.2.2

Multiply $5$ by $3$ .

$\frac{y^{15}}{2^{3}} {(2 y^{2})}^{4}$

Step 2.3

Raise $2$ to the power of $3$ .

$\frac{y^{15}}{8} {(2 y^{2})}^{4}$

Step 2.4

Apply the product rule to $2 y^{2}$ .

$\frac{y^{15}}{8} (2^{4} {(y^{2})}^{4})$

Step 2.5

Rewrite using the commutative property of multiplication.

$2^{4} \frac{y^{15}}{8} {(y^{2})}^{4}$

Step 2.6

Raise $2$ to the power of $4$ .

$16 \frac{y^{15}}{8} {(y^{2})}^{4}$

Step 3

Cancel the common factor of $8$ .

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Step 3.1

Factor $8$ out of $16$ .

$8 (2) \frac{y^{15}}{8} {(y^{2})}^{4}$

Step 3.2

Cancel the common factor.

$8 \cdot 2 \frac{y^{15}}{8} {(y^{2})}^{4}$

Step 3.3

Rewrite the expression.

$2 y^{15} {(y^{2})}^{4}$

Step 4

Multiply the exponents in ${(y^{2})}^{4}$ .

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Step 4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 y^{15} y^{2 \cdot 4}$

Step 4.2

Multiply $2$ by $4$ .

$2 y^{15} y^{8}$

Step 5

Multiply $y^{15}$ by $y^{8}$ by adding the exponents.

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Step 5.1

Move $y^{8}$ .

$2 (y^{8} y^{15})$

Step 5.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 y^{8 + 15}$

Step 5.3

Add $8$ and $15$ .

$2 y^{23}$